Logical relations for monadic types

JEAN GOUBAULT-LARRECQ, SŁAWOMIR LASOTA, DAVID NOWAK
2008 Mathematical Structures in Computer Science  
Logical relations and their generalizations are a fundamental tool in proving properties of lambda-calculi, e.g., yielding sound principles for observational equivalence. We propose a natural notion of logical relations able to deal with the monadic types of Moggi's computational lambda-calculus. The treatment is categorical, and is based on notions of subsconing, mono factorization systems, and monad morphisms. Our approach has a number of interesting applications, including cases for
more » ... lculi with non-determinism (where being in logical relation means being bisimilar), dynamic name creation, and probabilistic systems.
doi:10.1017/s0960129508007172 fatcat:kdwv2ozha5hvnfbxer7uckbu34